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Wall H.S. — Analytic Theory of Continued Fractions
Wall H.S. — Analytic Theory of Continued Fractions

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Название: Analytic Theory of Continued Fractions

Автор: Wall H.S.

Язык: en

Рубрика: Математика/Анализ/Непрерывные дроби/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 433

Добавлена в каталог: 28.11.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel      36
Approximant      15
Approximant as Stieltjes transform      254
Approximant of positive definite continued fraction      72
Approximant, elements in parabolic domains      136
Approximant, values in circular domain      42 46 60
Arzela      104
Associative law for bounded matrices      221
Asymptotic equality      316
Asymptotic equality between J-fraction and equivalent function      318
Asymptotic equality between power series and J-fraction      321
Asymptotic equality in angular domain      324
Asymptotic equality on imaginary axis      324
Bessel function      349
Beth      235
Bilinear form      216
Bilinear form, completely continuous      236
Blaschke      105
Bounded analytic functions in unit circle      283 285
Bounded analytic functions, chain sequences      279ff.
Bounded analytic functions, imaginary part negative      299
Bounded analytic functions, integral formulas for      275
Bounded analytic functions, real part positive      279 288
Bounded analytic functions, reciprocal of      280
Bounded J-fraction      119ff.
Bounded J-fraction, bound      111
Bounded J-fraction, convergence of      112 114
Bounded J-fraction, convex set for      113
Bounded J-fraction, norm      111
Bounded transformation      220
Bray      239
C-fraction      400
C-fraction, $\alpha$-regular      409
C-fraction, examples      403—405
C-fraction, regular      405
Cardioid theorem      142
Carleman      109 238 330
Carleman’s inequality      330
Carleman’s theorem on the moment problem      330
Cesaro mean      310
Chain sequence      79
Chain sequence, bounded analytic functions      278 288
Chain sequence, constant term      79
Chain sequence, maximal parameters positive      82
Chain sequence, minimal and maximal parameters      80
Chain sequence, moment problem for (0,1)      263
Chain sequence, parameters determined uniquely      82
Chain sequence, parameters of      79
Chain sequence, quadratic forms      86
Chain sequence, real J-fraction of norm $\leq 1$      115
Computation of roots of polynomials      185
Condition (H), necessary for convergence      122
Condition (H), theorem on sufficiency of      123
Continued fraction equivalent to a series      17
Continued fraction for certain divergent power series      350
Continued fraction of Gauss      337
Continued fraction of Gauss, convergence of      339
Continued fraction of Gauss, inequalities for      342
Continued fraction, expansions for functions bounded in unit circle      285
Continued fraction, expansions for functions in Ext $(-1,-\infty)$      279 288
Continued fraction, expansions for rational functions      161
Continued fraction, generated by linear transformations      14
Continued fraction, of Gauss      337
Continued fraction, of Pade table      380
Continued fraction, positive definite      67
Continued fraction, special type      45 48 64 103 116 118 285 289
Contraction formulas      22
Convergence continuation theorem      108
Convergence neighborhood      62 137
Convergence of continued fraction in cardioid domain      142
Convergence of continued fraction in the determinate case      110
Convergence of continued fraction in the indeterminate case      103 104
Convergence of continued fraction of Stieltjes      120
Convergence of continued fraction, condition (H)      123
Convergence of continued fraction, definition of      16
Convergence of continued fraction, exterior to cut      138
Convergence of continued fraction, necessary condition for      28 29 33
Convergence of continued fraction, periodic      37
Convergence of continued fraction, sufficient condition for      34 35 42 45 48 49 51 57 58 62 72 103 104 112 114 115 116 120 123 131 137 138 142 143 209 339 350 351
Convergence of continued fraction, uniform      16 42 45 48 49 131
Convergence of continued fraction, when partial numerator is zero      26 42 137
Convergence of continued fraction, whose elements have limits      138 139 339
Convergence of even (odd) part      53
Convergence of positive definite J-fraction, determinate case      110
Convergence of positive definite J-fraction, indeterminate case      104
Convergence of Stieltjes type continued fraction      120 123 131
Convergence problem      16
Convergence problem, general remarks on      25ff.
Convergence problem, nature of      27
Convergence set      45
Convergence set in parabolic domains      142
Convergence set, symmetric to real axis      58
Convergent      see “Approximant”
Convex extension      265
Convex set      113 137 237
Convex set, containing roots of polynomial      176
Convexity      264
de la Vallee Poussin mean      280
Dennis      51
Denominator      15
Denominator, different from zero      41 137
Denominator, expressed as determinant      65
Denominator, inequalities for      55
Determinant formula      16
Determinate case      99
Determinate case, convergence in the      110
Determinate case, sufficient conditions for      109
Determinate case, uniqueness of bounded reciprocal      234
Differential equation, Laguerre’s      412
Differential equation, power series solution      360 361
Dines      263
Divergence of continued fraction      16
Divergence of continued fraction, sufficient conditions for      27 28 29 33
Elements      14
Equivalence transformation      19
Equivalent function of J-fraction      231
Equivalent function of J-fraction, estimates for      235
Equivalent function of J-fraction, proper      254
Equivalent function of J-fraction, represented by Stieltjes transform      253
Euler      18
Euler — Knopp mean      309
Evans      239
Even part of continued fraction      20
Even part of continued fraction, convergence of      53
Expansion algorithm for test-fraction      175
Expansion algorithm of Stieltjes      203
Expansion algorithm, power series into C-fraction      401
Expansion algorithm, power series into J-fraction      198
Expansion algorithm, rational function into J-fraction      163
Expansion algorithm, rational function into S-fraction      171
Extension formulas      22
Formal integration      192
Forms, bilinear      216
Forms, linear      214
Forms, quadratic      222
Forms, unit      216
Frank      178 400
Frobenius      378
Functions of bounded variation      241
Functions with natural boundary      414
Functions, analytic exterior to cut      209
Functions, Bessel      349
Functions, binomial      343
Functions, elliptic      211 374 375
Functions, equivalent of J-fraction      231
Functions, error      357 358
Functions, exponential      348 349 367
Functions, hyperbolic      206 366 369—372
Functions, hypergeometric      335
Functions, incomplete gamma      356
Functions, logarithmic      200 342 343 344
Functions, meromorphic      209 347
Functions, nondecreasing      246
Functions, proper equivalent functions      254
Functions, psi function      372 373
Functions, quasi-analytic      330
Functions, represented by Stieltjes transform      247 253 254
Fundamental inequalities      40
Fundamental inequalities, first interpretation      42
Fundamental inequalities, second interpretation      54
Fundamental recurrence formulas      15
Gamma function, incomplete      356
Gamma function, Stieltjes continued fraction for      365
Green’s formula      96
Grommer      238
Gronwall      280
hadamard      399 412
Hadamard gaps      411
Hamburger      29 94 101 123 132 238 321
Hausdorff      761 111
Hausdorff inclusion problem      311
Hausdorff means      304
Hausdorff means, convergence preserving      307
Hausdorff means, examples of      309
Hausdorff means, form of      306
Hausdorff means, regular      309
Hellinger      69 95 96 98 109 214 233 235 238
Herglotz      275
hilbert      214 238 245
Hilbert space      215
Hilbert sphere      215
Hitchcock      185
Holder mean      310
Hypergeometric series      335
Indeterminate case      99
Indeterminate case, convergence theorem for      101
Inequalities, for denominators      55
Inequalities, for roots of polynomials      177
Inequalities, fundamental      40
Integral representation of analytic functions      275
J-form      103
J-form with five diagonals      334
J-form, bounded      111
J-form, norm      111
J-fraction      103
J-fraction for rational function      161
J-fraction for rational function, condition for existence      165
J-fraction for rational function, expansion algorithm      163
J-fraction for rational function, relation to power series      166
J-fraction, bounded      110ff
J-fraction, equal to power series      208
J-fraction, equivalent function of      231
J-fraction, even part of Stieltjes continued fraction      119
J-fraction, formally equal to $\rho_{11}$      213
J-fraction, indeterminate case      103
J-fraction, moments of      197
J-fraction, positive definite      104
J-fraction, power series expansion of      197
J-fraction, real      114
J-matrix      226
J-matrix for positive definite J-fraction      230
J-matrix, arbitrary      229
J-matrix, bounded      226
J-matrix, uniqueness of bounded reciprocal      234
Laguerre      412
Laguerre’s differential equation      412
Lambert’s continued fraction      349
Lane      36 61 91 148
Least squares      211
Legendre polynomials      344
Leighton      27 31 400
Limit-point and limit-circle cases      73
Linear forms      214
Linear systems      223
Linear transformations in infinitely many variables      212
Linear transformations in unit circle      286
Linear transformations, bounded      220
Linear transformations, fixed points of      36
Linear transformations, product of      13 36
Majorant series      41
Majorant series, divergent      54
Mall      29 31 132
Matrices, bounded      218
Matrices, Cesaro      301
Matrices, completely continuous      236
Matrices, Hausdorff      304
Matrices, J-matrices      226
Matrices, norm of      218
Matrices, permutable      302
Matrices, product      219
Matrices, reciprocal (right, left)      223
Matrices, sum      219
Matrices, symmetric      222
Matrix calculus      214
Moment problem      258
Moment problem for a finite interval      258 271
Moment problem for a finite interval, geometric characterization      265
Moment problem for a finite interval, normalized solution      259
Moment problem for a finite interval, solution by S-fractions      260
Moment problem for a finite interval, symmetrical      259
Moment problem for a finite interval, totally monotone sequences      267
Moment problem for an infinite interval      325
Moment problem for an infinite interval, Carleman’s theorem on      330
Moment problem for an infinite interval, determinate and indeterminate      326
Moments of J-fraction      197
Montel      105
Montessus de Balloire      412
Nest of circles $K_p(z)$      71
Nest of circles $K_p(z)$, radius $r_p(z)$      74—75
Nevanlinna, F.      334
Nevanlinna, R.      238 321 324
Norm, J-form      111
Norm, J-fraction      111
Norm, matrix      218
Notation for continued fraction      17
Numerator      15
Odd part of continued fraction      21
Odd part of continued fraction, convergence of      53
Orthogonal polynomials      193
Osgood      104
pade      378
Pade approximant      378
Pade approximant, degree of      388
Pade table      378
Pade table, block of order r      394
Pade table, diagonal files      393
Pade table, for series of Stieltjes      389
Pade table, general theorems on      393
Pade table, horizontal files of      412
Pade table, normal      379 388 399
Pade table, square in      389
Pade table, stairlike files in      380
Parabola theorem      58
Parabola theorem, connection with positive definite continued fraction      75
Parabola theorem, extension of      142
Parabola theorem, question of uniform convergence      78
Parabolic domains      58
Parabolic domains, family of      135 152
Partial denominator      14
Partial denominator, equal to zero      27
Partial fraction development, real J-fractions      115
Partial fraction development, Stieltjes continued fractions      120
Partial numerator      14
Partial numerator, equal to zero      26 42 72
Partial quotient      14
Paydon      44 48 79 137
Periodic continued fraction      23
Periodic continued fraction, convergence and value      37 39 190
Perron      22 36 48 50 137 412
Polynomials with real roots      172
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